An axially moving string system which is widely used in engineering equipment has attracted much attention for its transverse vibration problem affecting the normal operation of the equipment. For an axially moving string system with nonclassical boundaries， the analytical solution of the displacement response and energy at any propagating cycle is extended by applying the traveling wave reflection superposition method with a given uniform harmonic excitation force and initial conditions. The method of vibration suppression by the boundary control has the advantages of simplicity and economy. By installing the sensor， controller and actuator at the boundary， the control force is designed based on the optimal damping value and the vibration suppression of the reflected traveling wave. The transverse vibration is quickly suppressed after the first propagating cycle. During free and forced vibration of an axially moving string， the effectiveness of vibration suppression is demonstrated by simulations.